In Edward Albee's The Lady from Dubuque, just revived in London, a character notes culture's current concern with mortality: "That growing pile of books on how to die." Near the top of that heap, for quality and impact, would be Joan Didion's memoir of bereavement, The Year of Magical Thinking, which Didion has reshaped and updated into a theatrical monologue, performed by Vanessa Redgrave in a Broadway premiere directed by David Hare.

Didion is both a novelist and a reporter but, in The Year of Magical Thinking, brings her journalistic scrutiny to events which, in fiction, would be dismissed as manipulative melodrama. The book describes the sudden death of her husband, writer John Gregory Dunne, immediately after the couple had visited their gravely ill daughter, Quintana, in hospital. Since the published memoir was completed, Quintana has also died, and the 100-minute theatre-piece examines the double horror of burying a partner and a child within two years.

The play is remarkable, as the book was, for bringing to such bleak material an unexpected and unpredictable tone. Reportorial precision for the exact names of sinister diseases and the drugs to treat them alternates with playfulness and even humour. You wouldn't expect a handful of theatre-filling laughs in a piece about someone losing the two people she loved most, but Didion achieves them through gallows gags involving a brutally misunderstood crossword clue and a tactless sign in an intensive care unit.

If the play has a weakness, it is that there is an occasional unease in the fact that a book of private, writerly memoir inevitably becomes a phenomenon of public, performing memory. Confession is a first-person form; mediated by a performer, it becomes second-hand.

Respecting this problem, though, Redgrave and Hare have kept their interventions to a minimum, centering on Didion's words. The actress, who can be fidgety on stage, is still and precise, rarely leaving the slatted wooden chair which is the only prop, and her vocal flourishes are also sensibly rationed.

The reporter in Didion would have noted with some pleasure two aspects of the audience at the performance I saw. The level of attention was such that there was almost no coughing, when some Broadway auditoria resemble a TB ward; and many couples instinctively huddled close for warmth against the play's terrible intimations. It was a proper tribute to a remarkable, cathartic drama, in which a great writer files from her emotional warzone and a charismatic actress humbly helps her words into a wider world.